The subgradient extragradient method for solving variational inequalities in Hilbert space

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DOI10.1007/s10957-010-9757-3zbMath1229.58018OpenAlexW1991765628WikidataQ34776623 ScholiaQ34776623MaRDI QIDQ535068

Simeon Reich, Yair Censor, Aviv Gibali

Publication date: 11 May 2011

Published in: Journal of Optimization Theory and Applications (Search for Journal in Brave)

Full work available at URL: http://europepmc.org/articles/pmc3073511

zbMATH Keywords

variational inequalities nonexpansive mapping subgradient extragradient method weak convergence theorems

Mathematics Subject Classification ID

Variational inequalities (global problems) in infinite-dimensional spaces (58E35)

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feasibility problem ⋮ Convergence of the modified extragradient method for variational inequalities with non-Lipschitz operators ⋮ New extragradient-like algorithms for strongly pseudomonotone variational inequalities ⋮ Inertial projection and contraction algorithms for variational inequalities ⋮ The extragradient method for solving variational inequalities in the presence of computational errors ⋮ Extragradient method in optimization: convergence and complexity ⋮ Algorithms with strong convergence for a system of nonlinear variational inequalities in Banach spaces ⋮ Algorithms for a system of general variational inequalities in Banach spaces ⋮ Applications of fixed-point and optimization methods to the multiple-set split feasibility problem ⋮ A proximal point algorithm for finding a common zero of a finite family of maximal monotone operators in the presence of computational errors ⋮ Extragradient methods for solving non-Lipschitzian pseudo-monotone variational inequalities ⋮ Selective projection methods for solving a class of variational inequalities ⋮ Strong convergence of a modified extragradient method to the minimum-norm solution of variational inequalities ⋮ A modified projected gradient method for monotone variational inequalities ⋮ Strong convergence of the Halpern subgradient extragradient method for solving variational inequalities in Hilbert spaces ⋮ Algorithms for the split variational inequality problem ⋮ A hybrid method without extrapolation step for solving variational inequality problems ⋮ Inertial subgradient extragradient algorithms with line-search process for solving variational inequality problems and fixed point problems ⋮ Two strong convergence subgradient extragradient methods for solving variational inequalities in Hilbert spaces ⋮ Iterative method with inertial for variational inequalities in Hilbert spaces ⋮ Two new extragradient methods for solving equilibrium problems ⋮ Strong convergence result for solving monotone variational inequalities in Hilbert space ⋮ Strong convergence of a double projection-type method for monotone variational inequalities in Hilbert spaces ⋮ Strong convergence of double-projection method for variational inequality problems ⋮ Two-step methods and relaxed two-step methods for solving the split equality problem ⋮ On the weak convergence of the extragradient method for solving pseudo-monotone variational inequalities ⋮ A modified subgradient extragradient method for solving the variational inequality problem ⋮ An inertial subgradient-type method for solving single-valued variational inequalities and fixed point problems ⋮ A version of the mirror descent method to solve variational inequalities ⋮ Strong convergence of an extragradient-type algorithm for the multiple-sets split equality problem ⋮ Numerical approach to monotone variational inequalities by a one-step projected reflected gradient method with line-search procedure ⋮ Improved subgradient extragradient methods for solving pseudomonotone variational inequalities in Hilbert spaces ⋮ Regularization projection method for solving bilevel variational inequality problem ⋮ A modified subgradient extragradient method for solving monotone variational inequalities ⋮ A subgradient extragradient algorithm for solving multi-valued variational inequality ⋮ A two-step extragradient-viscosity method for variational inequalities and fixed point problems ⋮ A self adaptive inertial subgradient extragradient algorithm for variational inequality and common fixed point of multivalued mappings in Hilbert spaces ⋮ On the auxiliary mappings generated by a family of mappings and solutions of variational inequalities problems ⋮ Halpern projection methods for solving pseudomonotone multivalued variational inequalities in Hilbert spaces ⋮ A novel inertial projection and contraction method for solving pseudomonotone variational inequality problems ⋮ Weak convergence of iterative methods for solving quasimonotone variational inequalities ⋮ Modified inertial subgradient extragradient method in reflexive Banach spaces ⋮ ``Optimal choice of the step length of the projection and contraction methods for solving the split feasibility problem ⋮ A parallel extragradient-like projection method for unrelated variational inequalities and fixed point problems ⋮ Self-adaptive inertial extragradient algorithms for solving variational inequality problems ⋮ New algorithms and convergence theorems for solving variational inequalities with non-Lipschitz mappings ⋮ Iterative algorithms for solving fixed point problems and variational inequalities with uniformly continuous monotone operators ⋮ Modified subgradient extragradient method for variational inequality problems ⋮ Inertial shrinking projection algorithm with self-adaptive step size for split generalized equilibrium and fixed point problems for a countable family of nonexpansive multivalued mappings ⋮ Analysis of versions of relaxed inertial projection and contraction method ⋮ Strong convergence theorems for solving variational inequality problems with pseudo-monotone and non-Lipschitz operators ⋮ Convergence of one-step projected gradient methods for variational inequalities ⋮ A new extragradient-type algorithm for the split feasibility problem ⋮ Strong convergence inertial projection algorithm with self-adaptive step size rule for pseudomonotone variational inequalities in Hilbert spaces ⋮ An inertial subgradient extragradient algorithm extended to pseudomonotone equilibrium problems ⋮ Convergence theorem for system of pseudomonotone equilibrium and split common fixed point problems in Hilbert spaces ⋮ An iterative algorithm for solving variational inequality, generalized mixed equilibrium, convex minimization and zeros problems for a class of nonexpansive-type mappings ⋮ Modified modulus-based matrix splitting algorithms for a class of weakly nondifferentiable nonlinear complementarity problems ⋮ On the analysis of variance-reduced and randomized projection variants of single projection schemes for monotone stochastic variational inequality problems ⋮ A projected extrapolated gradient method with larger step size for monotone variational inequalities ⋮ Explicit extragradient-like method with adaptive stepsizes for pseudomonotone variational inequalities ⋮ Two strongly convergent self-adaptive iterative schemes for solving pseudo-monotone equilibrium problems with applications ⋮ Variance-based subgradient extragradient method for stochastic variational inequality problems ⋮ Strong convergence of the modified inertial extragradient method with line-search process for solving variational inequality problems in Hilbert spaces ⋮ On modified subgradient extragradient methods for pseudomonotone variational inequality problems with applications ⋮ An algorithm for finding a common point of the solutions of fixed point and variational inequality problems in Banach spaces ⋮ A new algorithm for solving multi-valued variational inequality problems ⋮ Convergence of relaxed inertial subgradient extragradient methods for quasimonotone variational inequality problems ⋮ Two nonmonotonic self-adaptive strongly convergent projection-type methods for solving pseudomonotone variational inequalities ⋮ A Tseng extragradient method for solving variational inequality problems in Banach spaces ⋮ Modified inertial projection and contraction algorithms for solving variational inequality problems with non-Lipschitz continuous operators ⋮ A simple algorithm for computing projection onto intersection of finite level sets

Cites Work

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